Performing measurement or calibration on positioning machines

ABSTRACT

Apparatus which can be used to calibrate a machine or as a machine itself includes two structures, each with three supports spaced in a triangular array thereon. The supports may be balls or sockets. The structures are interconnected by six members, and each support has the ends of two members connected to it. When used as a calibration device, the members are passive extensible measuring bars and the structures are respectively connected to fixed and movable parts of a machine so that movement of the machine parts causes relative movement between the structures and varies the lengths of the measuring bars. From measurements of the lengths of the measuring bars the actual movement of the machine part can be calibrated. When used as a machine, the members are powered struts by means of which one of the structures, which carries a tool or a probe can be manipulated relative to the other, to position the tool or probe relative to a workpiece.

BACKGROUND OF THE INVENTION

This invention relates to machines in which one member is positionedrelative to another. For example, it relates to coordinate measuringmachines, machine tools, scanning machines and robots, in which a toolor probe is positioned relative to a workpiece.

More particularly, the invention relates to performing measurements orcalibration on such machines.

In some aspects, the present invention is a development of the apparatusand methods described in our International Patent Application No.PCT/GB94/02593, published as WO95/14905 to which reference should bemade. Reference is also directed to the apparatus and methods describedin International Patent Applications Nos. WO91/03145 (Kearney & Trecker)and WO92/17313 (Geodetic Machines), and in European Patent ApplicationNo. 534585 (Ingersoll).

All the above applications show machines in which a tool, probe or otheroperator is mounted on one structure, for movement relative to anotherstructure upon which a workpiece may be mounted. The tool, probe orother operator may be movable and the workpiece fixed, or vice versa.The relative movement is effected by six rams acting between the twostructures. These rams can be controlled so as to produce any desiredrelative movement between the structure, with six degrees of freedom(three translational and three rotational). It is necessary to measurethe movements of the rams, and one aspect of the present invention isconcerned with such measurement.

A problem with the apparatus described in the various above-referencedpatent applications is that of calibrating the movement of the machine.To achieve this, it is necessary to measure the relative position andorientation of the moving structure relative to the fixed structure,independently of the measurements of the extensions of the rams whichproduced that position and orientation. Another aspect of the presentinvention allows such calibration, both on the type of machine describedin the above patent applications, and on more conventional machines.

SUMMARY OF THE INVENTION

According to one aspect of the present invention a method of calibratinga machine comprises the steps of attaching a first structure to one partof a machine, said structure having at least one spherical orpart-spherical support thereon,

attaching a second structure to a second part of a machine, saidstructure having three spherical, or part-spherical supports thereonarranged in a triangular pattern,

interconnecting the two structures by at least three measuring bars eachof which is attached to one of the supports on each structure,

producing relative movement between the two parts of the machine therebycausing relative movement between the two structures, determining thechanges in the lengths of the measuring bars caused by the relativemovement of the two structures, and

determining from such length changes the actual movements of the twostructures.

According to one embodiment of the invention the first structure hasthree spherical or part-spherical supports thereon which are arranged ina triangular pattern, six measuring bars are provided, opposite ends ofeach bar being connected to one support on each structure. In such anembodiment, each support on both structures has the ends of twomeasuring bars connected to it.

According to another embodiment of the invention, the first structurecomprises a single support disposed on the machine at the position whichwould normally be occupied by the tip of a tool or a measuring probe,three measuring bars are provided, opposite ends of each bar beingconnected to the single support on the first structure, and to one ofthe supports on the second structure.

According to another aspect of the invention there is provided apparatuscomprising a first structure having at least one spherical orpart-spherical support thereon, a second structure which has threespherical or part-spherical supports spaced in a triangular patternthereon, and at least three members interconnecting the two structures.

The apparatus may be connected to a machine as a calibration device inwhich case the members may be passive measuring bars, or alternativelythe members may be powered extensible struts capable of manipulating oneof the structures relative to the other.

In one embodiment of the invention both of the structures have threespherical or part-spherical supports spaced in a triangular patternthereon, and six members are provided, each of which is connected at oneof its ends to a support on one of the structures and at the other ofits ends to a support of the other one of the structures. In such anembodiment each support on both structures has the ends of two membersconnected to it.

The powered struts may also incorporate measuring devices so that theyadditionally act as measuring bars for determining the relativemovements of the two structures.

In any of the above-described embodiments of any of the aspects of theinvention, the supports may take the form of spheres or part-spheres, orof spherical or part-spherical sockets. The supported ends of themeasuring bars or struts may therefore be provided with correspondinglyshaped balls or sockets at either end as appropriate, which may becompletely spherical or only part-spherical, in order to fit on thesupports.

The measuring bars or struts may extend between the supports and betelescopic or extensible in some other way, or may be of fixed lengthand extend through, or carry extensions which extend through, thesupports so as to provide a greater range of relative movement for thestructures.

The struts may be powered by internal or external drive means as knownper se.

According to one novel feature of the invention, the supported end of ameasuring bar or strut lies at an angle to the longitudinal axis of thestrut, whereby, when in position on the support, the axis of the strutis aligned with the centre of the support.

The measuring bars or struts may be attached to the supports in anyconvenient manner, but a preferred form of attachment is by means ofmagnetic attraction.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention will now be described withreference to the accompanying drawings, wherein:

FIG. 1 is a simplified isometric view of a preferred embodiment ofmeasurement or calibration apparatus,

FIG. 2 is a side view of part of the apparatus of FIG. 1,

FIG. 3 is a more detailed side view of another part of the apparatus ofFIG. 1,

FIG. 4 is a schematic perspective view of a modification of part of FIG.1,

FIG. 5 shows part of an alternative embodiment of the measurement orcalibration apparatus of the invention,

FIG. 6 is a detail of one of the ball and socket joints showing amodified socket,

FIG. 7 shows one way of attaching the ends of four struts to a singleball of the apparatus of the invention,

FIG. 8 shows a further embodiment of the invention,

FIG. 9 shows a modification to the embodiment of FIG. 8,

FIG. 10 shows an alternative embodiment of apparatus according to theinvention,

FIG. 11 is a part-sectional view in the direction of arrow A of FIG. 10showing detail of the attachment of two powered struts to the structure,

FIG. 12 is a section on line C--C of FIG. 11,

FIG. 13 is a part-sectional view in the direction of arrow B of FIG. 10showing detail of an alternative attachment of two powered struts to thestructure, and

FIG. 14 is a section on the lines D--D of FIG. 13.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows a device which can be used for calibration. It comprises anupper structure in the form of an open triangular frame 10 and a lowerstructure in the form of an open triangular frame 12. Each frame isprovided with three precision steel balls 14, one at each corner of thetriangle. In use, the upper frame 10 is clamped to the moving structureof a machine, while the lower frame is clamped to the fixed structure(or vice versa). The device may be used with conventional machine toolsor with the types of machines illustrated in the above-referencedInternational and European applications.

The spheres 14 are linked in use by six members which in this embodimentare passive measuring bars 16. The position of these are shown merely bybroken lines in FIG. 1, but more detail is seen in FIG. 3. Eachmeasuring bar 16 in this example comprises parts 18,20 which interfittelescopically and extend between the spheres, but may take the form ofrigid links which pass through the spheres as described in laterembodiments. At each end, there is provided a magnetic socket 22, whichholds the bar 16 in a universally pivotable manner to a respective oneof the balls 14. The length of the bar 16 at any given time is thereforean accurate measure of the distance between the balls 14. This length ismeasured by any convenient transducer system, for example a scale 24within the member 18, over which passes a readhead 26 attached to themember 20.

The magnetic sockets 22 are of a type which is known, and commonly usedin ball bars which are used for calibrating machines tools and otherpositioning machines. They contain a trihedral support into which theball 14 is drawn by a magnet. Given that the ball 14 is accuratelyspherical, the connection between the ball and the bar 16 is thusdefined kinematically with great precision. The magnetic sockets 22 aredescribed in, for example, U.S. Pat. No. 4,435,905 (Bryan) and in "ASimple Method For Testing Measuring Machines and Machine Tools" by J. B.Bryan, Precision Engineering, Vol 4, No. 2, April 1982, pages 61-69 andNo. 3, July 1982, pages 125-138. The magnetic sockets are not essentialand other forms of connection may be used.

In use, the triangular frames 10,12 are clamped to the fixed and movingparts of the machine by any convenient means, and the six measuring bars16 are placed between the respective balls 14. The machine is nowexercised so as to move the moving part to a number of differentpositions and orientations relative to the fixed part. As this happens,a computer as shown at 121 in FIG. 11 acquires data from the transducersin each of the measuring bars 16. Using known algorithms, this data isused to determine the precise position and orientation to which themachine has been moved, and thus to calibrate its motion. For example,it is possible to build up an error map showing the true position andorientation of the moving part of the machine for any given demandedposition as shown by its own measuring devices.

The upper and lower triangular frames 10,12 may each be built as asingle unit if desired. However, for convenience, we prefer that itshould be of modular construction, made up from a kit of parts which canbe dismantled for portability. As seen in FIGS. 1 and 2, therefore eachframe may be made up of three rods 28, with a screw connection 30 ateach end for attachment to the ball 14. If desired, the kit of parts formaking the apparatus of the present invention may include a selection ofrods 28 of different lengths, for use on machines of different sizes. Ofcourse, the frames 10,12 may also have various clamping features tofacilitate clamping to the machine, but these are not shown.

The algorithms used to determine the position and orientation of themachine from the lengths of the measuring bars 16 require that thedistances between adjacent balls 14 on each of the frames 10,12 shouldbe known. These distances may be determined using one of the measuringbars 16 itself, as shown in broken lines in FIG. 2. A total of six suchmeasurements are required before the calibration procedure is carriedout, three between adjacent pairs of balls on the frame 10, and threebetween adjacent pairs of balls on the frame 12.

The kit of parts may also include a calibration block so that themeasuring bars 16 can be calibrated before use. Such a calibration blockhas two precision steel balls, like the balls 14 connected together at aknown spacing. This known spacing may be separately calibrated to atraceable standard. The balls of the calibration block may be connectedtogether by a bar of a material having a low or zero coefficient ofthermal expansion, such as INVAR™, or ZERODUR™. This ensures that theknown spacing between the balls does not change with temperature.

Since each ball 14 of the frames 10,12 must receive the magnetic socketsof two of the measuring bars 16, it is necessary to ensure that they donot foul each other during movement. With a measuring bar as shown inFIG. 3, it may be necessary to use balls 14 which have a somewhat largerdiameter than the magnetic sockets 22, so that two such sockets can fiton one ball simultaneously.

The invention is not restricted to calibrating machines of the typeshown in the above-mentioned earlier patent applications. It can equallybe used for calibrating a conventional machine tool, coordinatemeasuring machine, robot, etc. Such conventional machines generallyinvolve a plurality of axes, arranged in series with each other. Forexample, a five axis machine tool or coordinate measuring machine mayinvolve three slide axes, X,Y,Z, plus two axes of rotation, A and B. Thepresent apparatus may be used to calibrate such a machine by connectingthe upper frame 10 to the spindle or quill of the machine, and the lowerframe 12 to the table or workpiece holder of the machine. FIG. 4illustrates schematically one way in which the upper frame 10 might beadapted to enable it to be easily fitted in a spindle or quill of such amachine. In addition to the six frame members 28, it also has threefurther links 34, in the form of a tetrahedron. At the apex of thetetrahedron, there is provided a spigot 36 for fitting in the machine'squill or spindle. This spigot may if desired be in the form of astandard taper shank as usually used for fitting tools into the spindleof a machine tool.

The apparatus described is not restricted to use for calibratingmachines. It can be installed permanently on a machine, forming themeans by which the position and orientation of the moving part of themachine is measured, in order to provide position feedback data for theservo control of the machine's movement. For example, it may replace theextensible instrument arms described in WO91/03145. The six measuringbars 16 of the present apparatus may also be mounted (on balls 14),parallel with the six rams 18 described in our International PatentApplication No. PCT/GB94/02593. They then replace the interferometers orother devices described in that application for measuring the machine'smovement.

Another possibility is for the upper frame 10 to form part of (or to beclamped to) a special metrology frame, which is separate from the movingpart of the machine, but connected to it so as to undergo the samemotions as the tool or probe. An example of such a separate metrologyframe is shown in FIG. 6 of our earlier International Patent ApplicationNo. PCT/GB94/02593. Instead of the upper frame 10 of FIG. 1 of thepresent application, the three balls 14 are simply connected at threespaced locations on the metrology frame 68 shown in FIG. 6 of theearlier application which thus forms the structure. If the measuringbars 16 of the present application are intended to form the permanentmeasuring devices for the machine, then the balls 14 of the presentapplication will simply be connected in place of the retroreflectors 66of the interferometers shown in FIG. 6 of that earlier application.

As an alternative to the triangular frames 10 and 12 shown in FIG. 1,there is shown in FIG. 5 a frame which consists of three rigid rods 40,each of which has a ball 42 permanently attached at one end and amagnetic socket 44 at the other end.

Other arrangements are possible in the construction of the triangularframes 10 and 12. For example the kit of parts described with referenceto FIG. 1 may consist of six balls, six rigid rods and six measuringbars. The rods and measuring bars terminate in magnetic sockets asdescribed so that they will snap onto the balls. The six rigid rods arearranged to form two rigid triangular frames for the top and bottom ofthe apparatus and the measuring bars are connected between thetriangular frames.

Clearly the balls and sockets can be interchanged in other embodimentswhile still providing the rigid triangular frames interconnected bymeasuring bars.

In FIG. 5 the triangular frame is illustrated in place in a calibrationjig 46 for determining the spacing of the balls. The jig, which may bemade from ZERODUR™ or INVAR™, includes one fixed socket 48 at one endand a movable socket 50 at the other end. The distance between thecentres of the sockets gives a measure of the distance between thecentres of the balls 42. This distance may be measured by a telescopingsensing device, for example an LVDT, as shown at 50, or a retroreflectormay be mounted on the movable socket to reflect a light beam from alaser interferometer system (not shown) mounted on the fixed socket tomeasure the distance between the balls interferometrically.

In the assembled metrology frame the magnetic sockets of the measuringbars 16 are attached to the balls 42.

It is preferable that the axes of the rods and measuring bars shouldpass through the centres of the balls 42. In order to accommodate thisfeature where three or more attachments are to be made to one ball, oneor more of the sockets on any arm, or on the rods, may be arranged at anangle to the axis of the rod or arm as shown in FIG. 6.

One of the rods 40 is shown in FIG. 6 attached to a ball 42. Each sockethas three pads 52 which make contact with the surface of the ball 42.One of the pads lies on the axis of the rod and thus contacts the ballon the line of the axis through the centre of the ball 42. The other twocontact points lie preferably just over the orthogonal centre lines ofthe ball from the first. A magnet 54 is set into the socket to hold thesocket in position on the ball.

The use of magnetically retained sockets in the two triangular frames10,12 makes them easy to dismantle for portability of the frame. Socketsas described with reference to FIG. 6 can be provided at both ends ofthe rods.

It is not however, essential that the structures are formed asassemblies of rods and balls. A solid or hollow triangular structurecould be provided with balls or part-spherical sockets at its apices.

FIG. 7 shows one arrangement of rods 28,(40) and measuring bars 16 ofthe above-described embodiments which enables two rods and two measuringbars to terminate on a single one of the balls 14,(42).

It can be seen that each of the rods 28,(40) in this example arestraight and terminate in magnetic sockets 22 which are concentric theaxes of the rods. The rods are attached to the ball 14,(42) with theiraxes aligned with the centre of the ball.

Each of the measuring bars 16 have angled sockets 60 similar to thoseillustrated in FIG. 6 which enable the measuring bars to be attached tothe ball 14,(42) with the axes of the bars passing through the centre ofthe ball. Magnets 62 are provided in the sockets to hold the bars inplace. The sockets are positioned on the ball to enable the maximumfreedom for pivoting movement of the measuring bars without interferenceas the two triangular frames are moved relative to one another on themachine being calibrated.

In accordance with another novel aspect of the invention shown in FIGS.8 and 9, the arrangement of FIG. 1 may be simplified. In place of anupper structure having three balls 14, the structure may consist of asingle ball 70. This should be mounted on the moving structure of themachine and where this is the spindle 72, it should be located inexactly the same position as will be occupied by the operative point ofthe tool which is to be used. For example, this may be at the locationof the cutting point of a cutting tool, or at the location of a stylustip of a contact sensing probe. The lower frame 12 remains as in FIG. 1,and a total of three measuring bars 16 are used. Each measuring bar isfitted between the single ball on the moving structure, and a respectiveone of the balls 14 of the frame 12. The machine is then exercised andcalibration data acquired in the same way as previously. However, withonly three measurements available, it is only possible to determine thespatial position of the ball on the moving structure, and not theorientation of the moving structure. That is the reason why it isnecessary to mount the ball on the moving structure at the same locationas the operative point of the tool.

In order to obtain information on roll, pitch and yaw of the movingstructure, a single ball 74 may be mounted on the moving structure bymeans of an extension 76 which extends laterally from the operativepoint of the tool (see ball 70 in FIG. 8) so that the single ball 74 isoffset from this point as shown in FIG. 9. The lower frame and measuringbars are connected to the fixed structure as shown in FIG. 8.

One method of obtaining the roll, pitch and yaw data is to calibrate themachine by performing a first calibration routine with the frame 12 andsingle ball 70 connected as shown in FIG. 8, and then leaving the frame12 in the same position, substituting the extension as shown in FIG. 9and repeating the calibration routine. Any difference in the resultswill indicate the roll, pitch and yaw data.

FIGS. 10 to 14 illustrate another embodiment of the invention in whichthe apparatus is capable of being used as a machine tool, a robot or ameasuring machine for positioning a tool or probe relative to aworkpiece. For this purpose the measuring bars are replaced by poweredstruts which may themselves incorporate measuring devices. In thisembodiment both of the upper and lower structures are triangular andcarry three supports.

Such powered struts are themselves known, per se and are not describedin detail. They may, for example be telescopic with internal drivemechanisms as illustrated in International Patent ApplicationWO91/03145, or they may pass through the triangular support, or haveextensions which do so, and be driven internally, as shown inInternational Patent Application No. WO92/17313, or externally as shownin FIG. 4 of our International Patent Application PCT/GB94/02593. Onenovel feature of the present invention lies in the manner in which thestruts are connected to the triangular structures so as to allow foraccurate measurement of the lengths of the struts.

FIG. 10 shows diagrammatically one example of the construction of thetriangular structures. In this example the top and bottom structures100,102 respectively are rigid solid or fabricated triangular structureshaving spherical sockets 104,106 respectively at each apex thereof. Thespherical sockets replace the balls described in the previousembodiments (although balls could be used) in order to simplify theconstruction of the machine.

The two triangular structures 100,102 are interconnected by six poweredstruts 108 as indicated by the broken lines. It can be seen that twostruts are connected to each of the sockets 104,106. The manner in whichthe struts are connected to the sockets is illustrated in FIGS. 11 to14.

FIGS. 11 and 12 show details of the connection of two struts to a ball112 at one of the sockets 104 in the top triangular structure 100, andFIGS. 13 and 14 show details of the connection of the other ends of thestruts to a ball 113 at one of the sockets 106 in the bottom structure102.

Referring now to FIGS. 11 and 12, it can be seen that the sphericalsocket 104 is formed in a cylindrical insert 110 which is split for easeof assembly, and supports a split ball bearing 112. The insert issecured in the structure 100 by a clamping plate 114 which clamps itagainst a ledge 116 in an aperture in the structure.

The struts 108 which may be square in cross-section (or have extensionswhich are of square cross-section), pass through apertures 111 in thesplit ball bearing 112, and are arranged so that one side of each strut(or extension) lies on the centre-line of the ball bearing. This flatsurface, in this example carries a scale indicated in part at 118 whichis read by a readhead 119, which may be opto-electronic or otherconvenient type, to determine the change in length of the strut. Thescale readings are passed via cables 120 to a computer 121 programmedwith appropriate algorithms known per se, in order to determine therelative positions of the balls 112 from the lengths of the struts atany instant.

Because the scale lies on the centre line of the ball baring, its changein length can be more accurately associated with any change in thedistance between the centre of the ball bearing 112 in structure 100,and the centre of the ball bearing 113 (described below) in structure102, as the two structures move relative to each other.

The struts in this example are driven by capstan drives at the ends ofthe struts outside the working volume of the machine. The capstan drivecomprises a drive roller 124 and a pair of pinch rollers 125 betweenwhich the strut is gripped. Each drive roller 124 is driven by a motor126 powered via cables 127 from an external source which may also becontrolled by the computer 121. The readheads 119 are mounted on themotor casing and this in turn is rigidly connected to the split ball 112by a rod 128 so as to rotate with the ball while allowing relativemovement between the scale on the strut and the readhead.

The struts in this embodiment are not telescopic or extensible but areof fixed length. Because they extend through the ball and out beyond thestructure 100, they allow for greater relative movements betweenstructures 100 and 102 than if they were telescopic struts confinedwithin the working volume of the machine.

Referring now to FIGS. 13 and 14 the connection of the opposite end ofeach strut to the socket 106 in structure 102 will be described.

As described with reference to socket 104, the socket 106 is formed in asplit cylindrical insert 130 clamped in position by a plate 132. Thecylindrical insert has a spherical internal surface to support the ballbearing 113 which is rigidly connected to an extension 131 on the end ofa first one of the struts 108a. This allows for universal pivotingmotion of the first strut 108a about the centre of the socket 106.

The second strut 108b has rigidly connected to its end an extension 136having an aperture therein with a spherical internal surface 138. Thissurface is supported on the spherical outer surface of a bearing element140 carried by a gudgeon pin 142 which passes through the sphericalbearing 134. This allows the strut 108b to be unaffected by pivoting ofthe strut 108a.

The bearing 113 is cut away to provide a slot 144 to receive theextension 136 and to allow a range of pivoting movement of the strut 108about the axis of the gudgeon pin 142. Because the gudgeon pin 142passes through the centre of the ball bearing 134 the strut is also ableto pivot independently about an orthogonal axis of the ball bearing 113.

The extensions 131 and 136 of the struts 108a and 108b respectively arearranged so that the surface which carries the scale 118 of each strutis aligned with the centre of the ball 113 while at the same time theaxis of each extension passes through the centre of the ball.

It is to be understood that the connections of the two ends of thestruts 108 at the sockets 104,106 in the two structures 100,102 arenecessarily different in this example where the struts are of fixedlength and have external drives.

Where the struts are telescopic or extensible in other ways and haveinternal drives as described in the International Patent Applicationsreferenced above, both ends of the struts could be connected asdescribed with reference to FIGS. 13 and 14. Other methods of connectingthe struts 108 to the structures 100,102 may of course be used alongwith other types of drive.

Other types of measuring transducers could be used and disposed eitherinternally or externally of the struts.

It is also to be understood that the different types of connectionsbetween struts and sockets, or measuring bars and balls are notessential or unique to the embodiments in which they are described, butmay in appropriate cases be interchanged between different embodiments.

Where the measuring bars alone are used relatively light magnetic forcesmay be utilised to maintain the bars in position on the balls. Where,however, a magnetic ball and socket arrangement is used to connect adriven strut to a plate or structure, the magnets will need to besufficiently powerful to prevent detachment of the strut from itssupport. In such circumstances, or in fact, in any of the ball andsocket embodiments, the ball and socket joint may be fed with air toproduce an air bearing effect to minimise friction.

It is also to be understood that a computer would be used to handle thedata coming from the transducers in the passive measuring bars althoughone has not been specifically identified in these embodiments.

Other of the embodiments of FIGS. 10 to 14 can also be read across tothe embodiments of FIGS. 1 to 9.

For example, to improve the amount of relative movement between theframes of the calibration device, the telescopic measuring bars 16 couldbe replaced by measuring bars of fixed length which pass through theballs 14 in similar manner to that illustrated for the powered struts inFIGS. 11 and 12.

I claim:
 1. A machine comprising:a pair of spaced structures; six strutsinterconnecting the structures; six ball and socket joints, with threeof said ball and socket joints being spaced in a triangular array oneach of said structures; each strut engaging at points spaced along itslength with a respective ball and socket joint on each of saidstructures, the spacing between said points defining a distance betweenthe centers of the ball and socket joints to which the strut isconnected; drive means associated with each strut for varying saiddistances; two struts being connected to each ball and socket joint,said struts extending through the ball and socket joints on one of saidstructures; and measuring devices, which are independent of the drivemeans, said measuring devices being provided in association with each ofsaid struts for determining said distances between the centers of theball and socket joints.
 2. The machine according to claim 1, whereineach measuring device comprises a scale which is read by a readhead. 3.The machine according to claim 2, wherein each strut or an extensionthereof includes a flat surface at least in a region which passesthrough a ball and socket joint and on which the scale is provided. 4.The machine according to claim 3, wherein each strut, or extensionthereof, is arranged so that said scale lies on a center line of theball and socket joint, and a longitudinal axis of each strut orextension thereof passes through the center of the ball and socketjoint.
 5. The machine according to claim 1, wherein said spacedstructures define a working volume of the machine and the drive meansfor the struts are provided on ends of the struts which lie outside saidworking volume of the machine.
 6. The machine according to claim 1,wherein ends of the struts are connected to the ball and socket jointson the other one of the structures with a longitudinal axis of eachstrut aligned with the centers of the ball and socket joints.